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Logic/Math

I know that expecting to hear intelligent commentary during a morning “news” program is like expecting to hear a Kardashian explain algebra, but I was still taken aback by a comment one of the lightweights on the Today show made yesterday. During a discussion about the San Bernardino shooting – in the midst of comments about how hard it is to report the news because “we’re also human beings” – one person tossed off the aside, “of course, we take our responsibility seriously as journalists…”

It stopped me in my morning tracks because my first thought was:

Do you? Do you really?

I do not think that means what you think it means.

If you took your job seriously, you would be reporting information instead of talking about how hard it is to not piss anyone off. Piss people off! You are the piss on the propaganda parade!

If you took your job seriously, you would report that the Second Amendment protects the right of the people to keep arms for the purpose of having a well-regulated Militia, rather than for every shit, giggle, and macho fantasy the NRA can imagine. Or that banning certain weapons, limiting stockpiles, and requiring safety standards does not contradict that commandment.

If you took your job seriously, you would point out that there is a difference between Hillary saying, “Everyone knew I was using a private server” while the President says, “We didn’t know she used it exclusively” (two statements that can both be true without conflict), and Trump saying, “I saw thousands of Muslims cheering on 9/11” (a statement that is patently, provably false). Spinning and lying may be a matter of degrees, but they are very important degrees – one is bitching about the A/C at work and the other is hypothermia.

If you took your job seriously, you would not let, “People agree with me,” be an acceptable argument. You would not report a politician or spokesperson’s claim, then cater to a false “balance” by reporting a counter claim and walking away without any discussion of which speaker – if any – is supported by fact.

If you took your job seriously, you would not report opinion polls, or Twitter wars, or YouTube trends; you would not interview every single victim of an assault, or speculate about what might be true when there is no information, or show every angle of footage in an orgy of tragedy porn.

If you took your job seriously, you would give us facts, statistics, what is known and not known… actual information.

Your job, reporters, is not to tell us what a certain percentage of us currently believe; your job is to give us the info we need to decide what to think going forward. News is not the same as story. Whether the public likes you personally doesn’t matter. Imbalance does not mean the same thing as bias – even if someone whines that it does.

And the problem with you forgetting all of that is this:

You are making us stupid.

Ignorance breeds fear, and fear breeds anger, and all of it adds up to the state of our world today.

Yes, we citizens have a responsibility as well. We need to call out those who remain willfully ignorant, lie, or deny facts; we need to make it socially unacceptable to act out of fear or anger or hate; we need to vote.

But when there is no island of responsible reporting to stand on amidst the sea of swirling bullshit, you make our job nearly impossible.

Exactly 100 years ago, an alien mind inside an unusual man opened the eyes of humanity and forever changed the way we see the universe. His name has become synonymous with Time and Relativity and Space, yet his face has appeared to the world in many different forms.

No, I’m not talking about The Doctor. At least not the one from Gallifrey.

Much like the Tenth and Eleventh Doctors, though, Doctor Einstein was also a hipster icon of his day. He may not have worn Chucks with a suit or made bow ties and the fez cool, but he did rock a thrift-shop wardrobe, some seriously crazy hair, and a retro bicycle as his regular ride.

Einstein was at times a frustrated genius, burdened – like the first few Doctors – by the inability of mere mortals to keep up with his intellect. He could also be patient and calm, like the Seventh Doctor, or grumpy like the Twelfth, and occasionally scare the shit out of people, much as the Fourth Doctor traumatized my childhood (no thanks to my older brother’s TV habits).

Like the Ninth Doctor (and the uncounted incarnation before him), Einstein was often a man reeling from and railing against war. But he also never lost his sense of whimsy – his inner Sixth Doctor – or (for some of us weirdos) his romantic appeal, like the Eighth.

Doctor Einstein saw and solved problems no one on this planet even conceived of, by keeping his mind open and letting his imagination lead the way. He quite often failed on the way to success, and knew that sometimes it is best to blow things up in order to put them back together much stronger. And 100 years ago, over the four Thursdays in November, 1915, he presented to the world his theory of General Relativity – quite literally creating the fabric of space-time with his mind.

I like to think of Einstein as the Zero-th Doctor – because any mathematician knows that counting really starts at zero, not one.

So today, as we celebrate family and friends, eat delicious meals, and give thanks for all that we have in this universe, spare a thought for the wonders of science. For the spaces we gather to share food, the gravitational pull that draws us together, and the time that slows down when life is really good.

And give thanks for Doctor Einstein, who opened our eyes to it all 100 years ago today. He is truly the original Time Lord.

Mae govannen, Mellon! Tolo ned; dortho. What’s that? You don’t speak Elvish? I said, “Well met, Friend! Come in; stay.” Don’t worry about which words mean what – just trust me; that’s the phrase. All you have to do is remember it, and you will speak Elvish too!

Okay, you’ll probably need a little more to get by, so if you run into trouble you should also remember Noro lim! (It means, “Run fast!”) Got it memorized? You may also want to practice saying them out loud so you can pedo (speak) well. If I’m throwing too much at you too fast, just ask me to daro (stop) – but I bet if you drill with some flashcards you’ll be able to absorb it soon enough.

Welcome to the Elvish-speaking world!

What, you don’t quite feel fluent? Of course you don’t; this is a completely ridiculous way to teach someone a language. Maybe you could hold down a job as a greeter at a Grey Havens jogging track (“Come in! Run fast!”). At best you could train an Elvish dog. But you certainly won’t be chatting with Elrond about the merits of mithril anytime soon.

If you have ever learned a language – and if you are reading this, I know you have – you know that an alphabet and some common phrases are not enough for conversation. We need vocabulary, and syntax. We need an understanding of the rules. In short, we need grammar.

And yet, for generations we’ve been teaching the language of math just like I taught you Elvish.

Learn those letters (digits 0 through 9); sing the alphabet so you can remember their order (counting); memorize these combinations and what they mean (drill those times tables); and BOOM. Good luck communicating!

The human brain is an amazing thing that can commit an impressive amount of information to memory – especially if it is useless – but after a certain point it just can’t memorize any more. Without some grammatical rules to govern things, the wheels rapidly fly off the Math Mobile. (At around fifth grade, for most people.)

Fortunately, education specialists know that learning logic is just as important for math “numeracy” as grammar is for literacy. Which is exactly what the Common Core sets as the new goal* of early math education.

[*I say “goal” because the Common Core is a collection of skill goals for each age and subject around which teachers and schools design specific curricula. It is not a set (or dictated) curriculum itself.]

Yeah, math homework looks really weird now, but that’s because – in addition to the old carry-the-one remainders method of doing math on paper – kids are first learning to think of numbers as collections and combinations of other numbers. They are learning the logic of math instead of just the labels. Like how a language speaker can look at a word she has never seen before and use prefixes, suffixes, and roots to figure out the definition anyway.

When a person who is “good at math” does subtraction or division in her head, she doesn’t line things up on top of or next to each other and fiddle around with carried numbers. No, she looks at your weird Facebook post celebrating your child’s 31st week of life and thinks that 31 is almost 32, which is itself made up of eight fours, and since there are four weeks in a month calculates that your child is just under eight months old because that’s the way normal people mark time, Thank You Very Much.

If that isn’t how you do math in your head, I am betting you probably don’t consider yourself “good at math.” Our kids, on the other hand, will be, and that will benefit everyone.

Is it annoying that future generations are going to know how to do stuff better than we can? Absolutely. Kids already think they know everything and this is only going to make them more obnoxious. But fighting against numeracy (or the Common Core in general) because “that’s not the way we learned it” makes about as much sense as going back to treating acne with urine. (Yeah, we used to do that apparently. Ew.)

Now, if you want to fight all the standardized testing, that’s a completely different issue. I will be right there burning the No. 2 pencils and bubble grids beside you. Tol acharn! (Vengeance comes!)

There need to be more math-inspired food holidays, and together you and I can make that happen.

Wasn’t Pi Day fun? Even though this year (3/14/15 at 9:26:53) was the Pi Day of the Century, March 14th is a great excuse to eat pie in any year. But, just as they say that there are 10 types of people in this world: those who understand binary and those who don’t, the world is also divided into those on team pie and team cake.

As much as I love the number pi, I am decidedly a cake girl. It was the source of great friction in a relationship once, even after I baked a Cherpumple to bridge the gap with my pie guy. (A Cherpumple is a cherry pie baked inside a chocolate cake on top of a pumpkin pie baked inside a spice cake on top of an apple pie baked inside a vanilla cake. It is a foot tall, weighs 18lbs and feeds about forty. Epic.)

So what other math-food holidays can we celebrate, preferably without sparking dessert wars?

We can stick to the irrational number world and celebrate “e Day”. Since e is the natural log, we could eat ants on a log, cheese logs, yule logs (the cake kind) and basically any other roulade. But e is approximated as 2.7, and February 7th has come and gone.

Famous ratios might be the answer, like the Pythagorean Theorem’s “a squared plus b squared equals c squared” relationship between the sides of a right triangle. This gives us the classic 3:4:5 triangle ratio, so we could have eaten triangular foods (pizza, baklava, candy corn) on March 4, 2005 (3/4/5) or June 8th, 2010 (6/8/10). Unfortunately, Pythagorean Theorem days require all three numbers, and even though the next one is September 12th, 2015 (9/12/15), I’M HUNGRY NOW.

Square root dates have the same need for three numbers that makes them rare – such as 2/2/4, 3/3/9, and next 4/4/16 – and besides, do we want an entire meal made up of root vegetables?

There is always the Fibonacci Sequence (my personal favorite), which runs 1,1,2,3,5,8,13… etc., adding the preceding two numbers into infinity. This number is traditionally celebrated on November 23rd (11/23), but could also be feted on 1/1/23 when it comes. Since Fibonacci formulated the sequence after a thought experiment about mating bunnies, we should all make like Elmer Fudd and hunt some wabbit.

Or, since the Fibonacci Sequence also defines the Golden Ratio – another irrational number, roughly 1.618 – we can celebrate the hell out of it on January 6, 2018. The rich can eat foods dusted in gold flakes and gold powder; the rest of us can meet up at McDonald’s.

Still, these dates are years away. I want math-inspired food NOW!

Our answer is the humble mole. Not the blind, hole-digging insectivore, nor the irritating, cancer-threatening skin growth; I mean the massive constant defined by the number of molecules in 12 grams of Carbon-12 – specifically 6.022 times 10 to the 23rd power.

Think about it: a mole is a unit of measurement in chemistry, and mole (“mo-lay”) is a delicious Mexican sauce made with chocolate and spices, so the food tie-in is natural and fantastic. Plus, the number of things in one mole of anything (6.022 x 10^23) is also known as Avogadro’s Constant; ‘Avogadro’ is so close to ‘avocado’ it’s like the food gods are daring us NOT to do this. A mole dish with avocado? Yes, please!

Finally, Amedeo Avogadro (for whom the number is named) was an Italian Count born in 1776 (freedom!) who studied and practiced law (litigiousness!) before inheriting his father’s title and enough money to retire and dick around with science (financial privilege!). What’s more American than that? This should absolutely be a national holiday.

Oh, sure, I know people already celebrate Mole Day on October 23rd at 6:02, but just as some people celebrate Pi Day on July 22nd (because it can also be approximated as 22/7 and Europeans write their dates day/month), we can certainly have two Mole Days. And, yes, it would make more sense to do it on June 2nd instead of June 22nd, but I missed that day, so screw it.

JOIN ME on June 22nd at 10:23 (am or pm is your choice) in eating a delicious Mexican dish of any type so long as it is slathered in mole sauce and accented with avocado.

If I could have one superpower, I would choose the ability to blink leaf blowers out of existence with my mind. My faithful sidekick would do car alarms. We would be The Sound and The Fury – fighting for peace, quiet, and the manual way.

Leaf blowers are stupid, especially in the city. They accomplish no more than a rake or broom, in barely less time, and do it all while polluting the air with ear-splitting noise and filthy dust. Gas-powered leaf blowers (which is most of them) do all of that while also spewing toxic fumes, making them simultaneously noisy and noisome.

‘Noisome’ is one of those words that makes no sense, because it should mean “loud” but instead means “offensively stinky or unpleasant”. That dissonance, though, is what makes it the perfect word to describe the current state of communication in our culture.

We have a problem with noisome discourse – increasingly disagreeable, foul, and loud – and just like the leaf blowers, the problem is largely fueled by GAS:

GENERALIZATIONS – all of which are terrible. (See what I did there?) Too often we inflate our arguments by shouting that “all cops are bad” rather than “this cop is bad” or that “all men are pigs” when at the moment only that man is a pig.

[Why is ‘pig’ a derogatory term? I love pigs. They are smart, and clean, and taste like bacon. We should all be pigs!]

The problem with arguments inflated by generalizations is that they are easily punctured by a single anecdotal counterexample – thus letting the air out of what may otherwise have been solid logic.

ASSUMPTIONS – which not only make asses out of us, but likewise also leak a noxious stench into the air. When we hear words leave a fellow human’s mouth these days (or see them typed), our instinct seems to be to immediately assume the most racist / sexist / elitist / ageist / atheist / anti-whatever-ist intentions behind them. Sure, taking offense is fun, but why not allow for the possibility someone is curious, mistaken, or just plain dumb instead of horrible? Assumptions are dangerous; it only takes a single spark of defensiveness to ignite an explosion of anger and send civility up in flames.

SELFISHNESS completes the toxic triumvirate in our GAS. Not just “shut up and let me talk,” selfishness, or the “my way or the highway” variety; we have also become selfish in our refusal to accept partial agreement or any personal fault. High on the fumes of our own opinion, we focus all our attention on winning that last minor point against an ally instead of working with them to battle the larger problems facing both of us. As with any gas, the overall pressure of selfishness increases as the force of our need to be 100% right gets divided by a smaller and smaller area of focus, ultimately resulting in a blowout.

This chemical cocktail of generalization, assumption, and selfishness is fueling a lot of sound and fury in our world today.

As science has shown, GAS will, once released, expand to fill any available space. It may not seem harmful at first, and is even tempting since GAS can burn colorful and bright or give us a quick high that makes life briefly hilarious. But it is not healthy to breathe and can quickly turn dangerous, which is why we should stop releasing GAS entirely.

It won’t be easy. GAS is often hard to hear, mostly impossible to see, and no one ever wants to admit it comes from them (even though we all do it). But GAS is filling our world with an odious cloud that is highly combustible, poisonous to ingest, and toxic to our environment.

On Earth Day, let’s all stop spewing this GAS into the air and let clearer heads prevail.

According to Schoolhouse Rock, three is a magic number – and it is. But just as pi is equal to a little more than three, pi itself is a little more than magical. It is downright metaphorical.

Mathematicians, scientists, and philosophers have been chasing down the elusive number for thousands of years. Pretty much since we gained awareness of numbers themselves, and round things. It didn’t take us long to figure out that the ratio between a circle’s circumference and its diameter was a constant number or that the number was just over three, but several hundred lifetimes would pass before we got more accurate than that.

What do you get when you divide the circumference of a jack o’ lantern by its diameter? Pumpkin pi!

The true quest for pi was borne out of our desire to “square the circle”. In a literal, mathematical sense this means finding a simple – or at least consistent – way to calculate a square with equal area to any given circle. Symbolically, squaring the circle is a much deeper human desire.

Circles have always been mysterious. They represent the infinite, even sometimes defined as “a polygon with infinite corners.” With no beginning or end point, they symbolize that which is eternal and immeasurable. According to Nietzsche and Matthew McConaughey, time itself is a flat one. Even this post is circular (it ends where it begins). Circles are unknowable, spiritual.

Squares, on the other hand, are a symbol of all that is solidly defined. They are firmly knowable, easily measured, comfortably comprehensible. There is a reason one of the earliest words in our culture for the nerdy and rule bound was “square.”

To search for an exact value of pi – to seek to square the circle – is to attempt to make the unknowable known. To define the undefined. Another term for pi is the “circular constant”, or in other words a mystery that is rock steady.

What was Sir Isaac Newton’s favorite dessert? Apple pi!

Historically, some have considered this quest to understand the mysterious a dangerous game. The poet John Donne wrote the verse, “Eternal God – for whom who ever dare / Seek new expressions, do the circle square, / And thrust into straight corners of poor wit / Thee, who art cornerless and infinite,“ explicitly condemning the search for an exact value for pi. Many more, like Archimedes, devoted their entire lives to the quest. All of them died without reaching it.

Because, of course, the quest is impossible. It took us several thousand years, but eventually (by the 18th century) we humans finally proved that the number pi is irrational – its digits go on forever and never repeat. About a hundred years later, we also determined that pi is transcendent, which means it is not the solution to any algebraic equation. Irrational and transcendent – just like the human mind.

Those two vital discoveries – that the circular constant is both never ending or repeating and impossible to equate – combine to prove without doubt that we cannot find a square with equal area to a circle. The circle, quite literally, can never be squared.

“Secant, tangent, cosine, sine, 3.14159!” – MIT cheerleaders

So the number pi is simultaneously proof that some things can never be known and that there are rock-solid constants we can rely on. Constants such as our drive to always dig deeper and know more, even if we can never understand it all. No wonder pi is the most enduringly studied number in human history.

These days, pi continues to symbolically bridge the mysterious and the defined. It has become our computational bedrock, used to test computers for bugs or weakness, and at the same time our mathematicians are scouring its digits through billions of decimal places (and counting!) in search of any pattern or logic to its order. So far, we’ve found nothing. It is proving uniquely and stubbornly random.

On March 14th, we celebrate this metaphorical number by eating pie, something both circular and delicious. We also celebrate another wonder of the universe – Albert Einstein, who was born on 3/14/1879. Einstein himself is a perfect representation of pi’s duality, as his life continuously bridged math and creativity, science and spirituality, and social consciousness with humor. He understood better than nearly anyone the perfect paradox embodied by pi: that the more we learn, the less we know.

Or, to put it in terms of the constant itself, “the wider the circle of light, the larger the circumference of darkness.” (Not an Einstein quote, but one of his favorites.)

TEN… By the time I was ten, I was madly in love with Albert Einstein. I have no idea how I even learned about him in the first place, but the source of my love was obvious. He was mischievous yet deeply profound, musical, passionate, curious, kind, odd looking, and more than a little alien; that is a vibe I could dig. My taste in men hasn’t changed much since.

NINE… In 9th grade, I decided to finally understand the Theory of Relativity. (Enough to do a report for school, at least.) My favorite illustration of how time is relative involves a flashlight and a train:

Imagine a light shining up from the floor of a moving boxcar, to a mirror on the ceiling. Turn the light on and it hits the mirror, bounces, and returns to the source. To an observer on the train with the light, the beam travels a distance equal to twice the height of the boxcar (up, then down).

But to an observer on a hill watching the train go by, the light travels further. Its journey isn’t just up and down, but also the horizontal distance the train travels in that time. To the observer on the hill, the light’s path is two diagonals of a triangle whose base is the distance traveled by the train and height is the height of the boxcar.

Since Rate (speed) is equal to distance divided by time, and since the speed of light is always the same, the fact that the light travels different distances means it also does so over different times. To the observer on the hill, the light’s journey took longer. More time passed than did for the observer on the train, even though they were both watching the same light.

EIGHT… This principle of relative time was demonstrated for a much wider audience in the 80’s, when a different Einstein – Doc Brown’s dog – spent a few seconds in a speeding DeLorean that simultaneously lasted a full minute for Marty McFly.

SEVEN… Any tween who was ever forced to play Seven Minutes in Heaven already understands the relativity of time with excruciating clarity. How slowly those seven minutes pass when we are awkward and self-conscious. Yet when I met Hodor earlier this year and we set a kitchen timer to 20 minutes on our second date (an attempt to wield some grown-up control over our teenage attraction) we were suddenly on a speeding train. Those minutes passed in seconds, and we had to reset the timer at least three more times to test its functionality (for the sake of science, of course).

SIX… I once even experienced the entire life-cycle of a relationship over the course of a six-hour conversation. Via text. It started as a chat about a basketball game, during which we acknowledged our usually moderate flirting had escalated to blatant, and then both admitted we were very interested in the person but not currently ready for the relationship. The raw honesty on display made me far more interested than at the start of the conversation, and our subsequent discussion about how to conduct ourselves in the future felt like passing through a break up and coming out the other side. In the course of one night, I gained an amicable divorce.

FIVE… Time is relative everywhere, not just in love (though especially in love). When I teach a five-hour logic class, I am most definitely on the train. Passage from start to end seems to take no time at all – though I know we traveled because I finish exhausted. My poor students experience the full expanse of the time, however, watching from the figurative hillside.

FOUR… Soon, we wave goodbye to the year 2014, a year full of time quirks. Looking at the bulk of events, we seem to have both traveled far and stood still. A lot of ugliness we thought was behind us turned out to be very present. But at the same time, the fact that we are now talking openly about things like religion, drugs, law enforcement, homophobia, sexism, racism, principles and so on is a huge step forward for our community.

THREE… For the first three months of 2014, I was an observer on the hill, living more life than my counterparts on the train. On January 1st I was a single girl between projects; by the end of March I had hundreds of regular readers and had both met and fallen completely for Hodor. For the last three months, I’ve been back on the train; Hodor left in September, but it feels like only days ago to me.

TWO… Career-wise, I ticked off a second full year of waiting for the biggest deal of my professional life to finalize. It is my own personal Groundhog Day – stuck reliving February 2nd when February 3rd is the day life starts. I fully understand why Bill Murray’s character experiments with violence in that movie.

ONE… December 31st is only one night, but somehow we imbue it with the weight of an entire year. With so much time passing in an instant, it is easy to feel bruised by the impact. But it is important to remember that the real significance of New Year’s Eve is…

ZERO. In almost every sense. It is nothing, a place-holder, just another day; it is also something, a baseline foundation from which to build another year. Zero can add nothing, nor can it take anything away. Yet it has the power to multiply things exponentially, or to negate them entirely.

It’s all in how we choose to use it. So, I say we use December 31st for a little bit of reflection, a whole lot of appreciation, and a healthy amount of celebration. Travel on the train or off, but remember it is still only one night, much as zero is only one number among many.

As long as zero isn’t also the amount of champagne left for drinking, everyone will be just fine.